Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2022, Cilt: 5 Sayı: ICOLES2021 Special Issue, 18 - 24, 30.11.2022
https://doi.org/10.34088/kojose.1050267

Öz

Kaynakça

  • [1] Samko S., Kilbas A., Marichev O., 1993. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Linghorne.
  • [2] Podlubny I., 1998. Fractional Differential Equations: An Introduction to Fractional Derivatives. Fractional Differential Equations to Methods of Their Applications vol. 198. Academic press.
  • [3] Lazarević M. P., Rapaić M. R., BŠekara T., 2014. Introduction to Fractional Calculus with Brief Historical Background. Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, WSEAS Press.
  • [4] Caputo M., Fabrizio M., 2015. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), pp. 73-85.
  • [5] Atangana A., Baleanu D., 2016. New fractional derivatives with non-local and non-singular kernel. Theory and Application to Heat Transfer Model, Thermal Science, 20(2), pp. 763-769.
  • [6] Atangana A., 2017. Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos Soliton. Fract.,102, pp. 396-406.
  • [7] Anderson G. D, Vamanamurthy M. K., Vuorinen M., 2007. Generalized convexity and inequalities, J. Math. Anal. Appl, 335, pp. 1294-1308.
  • [8] Kirmaci U. S., Bakula M. K, Özdemir M. E., Pecaric J., 2007. Hadamard type inequalities of s-convex functions. Applied Mathematics and Computation, 193, pp. 26-35.
  • [9] Bakula M. K, Özdemir M. E., Pecaric J., 2008. Hadamard type inequalities for m-convex and ( )-convex functions. Journal of Inequalities in Pure and Applied Mathematics, Volume 9, Issue 4, Article 96, 12pp.
  • [10] Dahmani Z., 2010. On Minkowski and Hermite-Hadamard integral inequalities via fractional integration. Ann. Funct. Anal., 1(1), pp. 51-58.
  • [11] Latif M. A., 2014. New Hermite-Hadamard type integral inequalities for GA-convex functions with applications. Analysis, 34(4), pp. 379-389, doi: 10.1515/anly-2012-1235.
  • [12] Özdemir M. E., Latif M. A., Akdemir A. O., 2016. On some hadamard type inequalities for product of two convex functions on the co-ordinates. Turkish Journal of Science, I(I), pp. 41-58.
  • [13] Atangana A., Koca I., 2016. Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order. Chaos, Solitons and Fractals, 89, pp. 447-454.
  • [14] Akdemir A. O., Ekinci A., Set E., 2017. Conformable fractional integrals and related new integral inequalities. J. Nonlinear Convex Anal., 18(4), pp. 661-674.
  • [15] Awan M. U., Noor M. A., Mihai M. V., Noor K. I., 2017. Conformable fractional Hermite-Hadamard inequalities via pre-invex functions. Tbilisi Math. J., 10(4), pp. 129-141.
  • [16] Atangana A., 2018. Non-validity of index law in fractional calculus: a fractional differential operator with Markovian and Non-Markovian properties. Physica A: Statistical Mechanics and its Applications, 505, pp. 688-706.
  • [17] Atangana A., Gomez-Aguilar J. F., 2018. Fractional derivatives with no-index law property: application to chaos and statistics. Chaos, Solitons and Fractals, 114, pp. 516-535.
  • [18] Deniz E., Akdemir A. O., Yüksel E., 2019. New extensions of Chebyshev-Pòlya-Szegö type inequalities via conformable integrals. AIMS Mathematics, 4(6), pp. 1684-1697.
  • [19] Akdemir A. O., Dutta H., Yüksel E., Deniz E., 2020. Inequalities for m-convex functions via -Caputo fractional derivatives. Matematical Methods and Modelling in Applied Sciences, 123, pp. 215-224, Springer Nature Switzerland.
  • [20] Akdemir, A. O., Karaoglan, A., Ragusa, M. A., Set, E., 2021. Fractional integral inequalities via Atangana-Baleanu operators for convex and concave functions. J. Funct. Spaces, Vol 2021, article ID 1055434, 10 p, https://doi.org/10.1155/2021/1055434.
  • [21] Dlamini A., Goufo E. F. D., Khumalo M., 2021. On the Caputo-Fabrizio fractal fractional representation for Lorenz chaotic system, AIMS Mathematics, 6(11), pp.12395-12421.
  • [22] Dragomir S. S., Pearce C. E. M, 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
  • [23] Toader G. H., 1984. Some generalizations of the convexity. Proceedings of the Colloquium on Approximation and Optimization, Cluj-Napoca, 329-338.

Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions

Yıl 2022, Cilt: 5 Sayı: ICOLES2021 Special Issue, 18 - 24, 30.11.2022
https://doi.org/10.34088/kojose.1050267

Öz

The main objective of this work is to establish new upper bounds for different kinds of convex functions by using fractal-fractional integral operators with power law kernel. Furthermore, to enhance the paper, some new inequalities are obtained for product of different kinds of convex functions. The analysis used in the proofs is fairly elementary and based on the use of the well known Hölder inequality.

Kaynakça

  • [1] Samko S., Kilbas A., Marichev O., 1993. Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Linghorne.
  • [2] Podlubny I., 1998. Fractional Differential Equations: An Introduction to Fractional Derivatives. Fractional Differential Equations to Methods of Their Applications vol. 198. Academic press.
  • [3] Lazarević M. P., Rapaić M. R., BŠekara T., 2014. Introduction to Fractional Calculus with Brief Historical Background. Advanced Topics on Applications of Fractional Calculus on Control Problems, System Stability and Modeling, WSEAS Press.
  • [4] Caputo M., Fabrizio M., 2015. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1(2), pp. 73-85.
  • [5] Atangana A., Baleanu D., 2016. New fractional derivatives with non-local and non-singular kernel. Theory and Application to Heat Transfer Model, Thermal Science, 20(2), pp. 763-769.
  • [6] Atangana A., 2017. Fractal-fractional differentiation and integration: connecting fractal calculus and fractional calculus to predict complex system. Chaos Soliton. Fract.,102, pp. 396-406.
  • [7] Anderson G. D, Vamanamurthy M. K., Vuorinen M., 2007. Generalized convexity and inequalities, J. Math. Anal. Appl, 335, pp. 1294-1308.
  • [8] Kirmaci U. S., Bakula M. K, Özdemir M. E., Pecaric J., 2007. Hadamard type inequalities of s-convex functions. Applied Mathematics and Computation, 193, pp. 26-35.
  • [9] Bakula M. K, Özdemir M. E., Pecaric J., 2008. Hadamard type inequalities for m-convex and ( )-convex functions. Journal of Inequalities in Pure and Applied Mathematics, Volume 9, Issue 4, Article 96, 12pp.
  • [10] Dahmani Z., 2010. On Minkowski and Hermite-Hadamard integral inequalities via fractional integration. Ann. Funct. Anal., 1(1), pp. 51-58.
  • [11] Latif M. A., 2014. New Hermite-Hadamard type integral inequalities for GA-convex functions with applications. Analysis, 34(4), pp. 379-389, doi: 10.1515/anly-2012-1235.
  • [12] Özdemir M. E., Latif M. A., Akdemir A. O., 2016. On some hadamard type inequalities for product of two convex functions on the co-ordinates. Turkish Journal of Science, I(I), pp. 41-58.
  • [13] Atangana A., Koca I., 2016. Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order. Chaos, Solitons and Fractals, 89, pp. 447-454.
  • [14] Akdemir A. O., Ekinci A., Set E., 2017. Conformable fractional integrals and related new integral inequalities. J. Nonlinear Convex Anal., 18(4), pp. 661-674.
  • [15] Awan M. U., Noor M. A., Mihai M. V., Noor K. I., 2017. Conformable fractional Hermite-Hadamard inequalities via pre-invex functions. Tbilisi Math. J., 10(4), pp. 129-141.
  • [16] Atangana A., 2018. Non-validity of index law in fractional calculus: a fractional differential operator with Markovian and Non-Markovian properties. Physica A: Statistical Mechanics and its Applications, 505, pp. 688-706.
  • [17] Atangana A., Gomez-Aguilar J. F., 2018. Fractional derivatives with no-index law property: application to chaos and statistics. Chaos, Solitons and Fractals, 114, pp. 516-535.
  • [18] Deniz E., Akdemir A. O., Yüksel E., 2019. New extensions of Chebyshev-Pòlya-Szegö type inequalities via conformable integrals. AIMS Mathematics, 4(6), pp. 1684-1697.
  • [19] Akdemir A. O., Dutta H., Yüksel E., Deniz E., 2020. Inequalities for m-convex functions via -Caputo fractional derivatives. Matematical Methods and Modelling in Applied Sciences, 123, pp. 215-224, Springer Nature Switzerland.
  • [20] Akdemir, A. O., Karaoglan, A., Ragusa, M. A., Set, E., 2021. Fractional integral inequalities via Atangana-Baleanu operators for convex and concave functions. J. Funct. Spaces, Vol 2021, article ID 1055434, 10 p, https://doi.org/10.1155/2021/1055434.
  • [21] Dlamini A., Goufo E. F. D., Khumalo M., 2021. On the Caputo-Fabrizio fractal fractional representation for Lorenz chaotic system, AIMS Mathematics, 6(11), pp.12395-12421.
  • [22] Dragomir S. S., Pearce C. E. M, 2000. Selected Topics on Hermite-Hadamard Inequalities and Applications. RGMIA Monographs, Victoria University.
  • [23] Toader G. H., 1984. Some generalizations of the convexity. Proceedings of the Colloquium on Approximation and Optimization, Cluj-Napoca, 329-338.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ebru Yüksel 0000-0001-7081-5924

Erken Görünüm Tarihi 30 Haziran 2022
Yayımlanma Tarihi 30 Kasım 2022
Kabul Tarihi 24 Şubat 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 5 Sayı: ICOLES2021 Special Issue

Kaynak Göster

APA Yüksel, E. (2022). Some Fractal-Fractional Integral Inequalities for Different Kinds of Convex Functions. Kocaeli Journal of Science and Engineering, 5(ICOLES2021 Special Issue), 18-24. https://doi.org/10.34088/kojose.1050267